# Intermediate Geometry : How to find the volume of a prism

## Example Questions

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### Example Question #95 : Prisms

The above figure shows a square pyramid inscribed inside a cube. The pyramid has volume 100. Give the volume of the cube.

Explanation:

Let  be the length of one side of the cube. Then the base of the pyramid is a square with sidelength , and its area is

.

The volume of a pyramid is one third the product of its height and the area of its base. The height of the pyramid is , so the volume is

The volume of the cube is , so

or, equivalently,

That is, the volume of the cube is three times that of the pyramid, and, since the pyramid has volume 100, the volume of the cube is .

### Example Question #96 : Prisms

A rectangular box has two sides with the following lengths:

and

If it possesses a volume of , what is the area of its largest side?

49

28

21

12

16

28

Explanation:

The volume of a rectangular prism is found using the following formula:

If we substitute our known values, then we can solve for the missing side.

Divide both sides of the equation by 12.

We now know that the missing length equals 7 centimeters.

This means that the box can have sides with the following dimensions: 3cm by 4cm; 7cm by 3cm; or 7cm by 4cm. The greatest area of one side belongs to the one that is 7cm by 4cm.

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